Weakly Semialgebraic Spaces (Lecture Notes in Mathematics, 1367, Band 1367) - Softcover

Knebusch, Manfred

Softcover

ISBN 10: 3540508155 ISBN 13: 9783540508151

Verlag: Springer, 2009

Inhaltsangabe

The book is the second part of an intended three-volume treatise on semialgebraic topology over an arbitrary real closed field R. In the first volume (LNM 1173) the category LSA(R) or regular paracompact locally semialgebraic spaces over R was studied. The category WSA(R) of weakly semialgebraic spaces over R - the focus of this new volume - contains LSA(R) as a full subcategory. The book provides ample evidence that WSA(R) is "the" right cadre to understand homotopy and homology of semialgebraic sets, while LSA(R) seems to be more natural and beautiful from a geometric angle. The semialgebraic sets appear in LSA(R) and WSA(R) as the full subcategory SA(R) of affine semialgebraic spaces. The theory is new although it borrows from algebraic topology. A highlight is the proof that every generalized topological (co)homology theory has a counterpart in WSA(R) with in some sense "the same", or even better, properties as the topological theory. Thus we may speak of ordinary (=singular) homology groups, orthogonal, unitary or symplectic K-groups, and various sorts of cobordism groups of a semialgebraic set over R. If R is not archimedean then it seems difficult to develop a satisfactory theory of these groups within the category of semialgebraic sets over R: with weakly semialgebraic spaces this becomes easy. It remains for us to interpret the elements of these groups in geometric terms: this is done here for ordinary (co)homology.

Über diesen Titel

Über die Autorin bzw. den Autor

¿Manfred Knebusch is Professor Emeritus at the University of Regensburg. He has written nine books and more than 80 papers on the algebraic theory of quadratic forms over rings and fields, valuation theory, real algebra and real algebraic geometry. His current research focusses on tropical geometry.

Claus Scheiderer is Professor at Konstanz University. His primary research interests are real algebraic geometry and convex algebraic geometry.

Thomas Unger is Associate Professor at University College Dublin. His research interests include quadratic and hermitian forms, algebras with involution, and noncommutative real algebra and geometry.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2009
• Sprache: Englisch
• ISBN 10: 3540508155
• ISBN 13: 9783540508151
• Einband: Taschenbuch
• Anzahl der Seiten: 400
• Kontakt zum Hersteller: GPSR Kontakt; ProductSafety@springernature.com; ; Tiergartenstr. 17; Heidelberg; 69121; Deutschland